The detection of smooth trajectories in a (noisy) point set sequence can be realized optimally with the ASTRE algorithm, but the quadratic time and memory complexity of this algorithm with respect to the number of frames is prohibitive for many practical applications. We here propose a variant that cuts the input sequence into overlapping temporal chunks that are processed in a sequential (but non-independent) way, which results in a linear complexity with respect to the number of frames. Surprisingly, the performances are in general not affected by this acceleration strategy, and are sometimes even slightly above those of the original ASTRE algorithm.